1 Progress In Electromagnetics Research, PIER 6, 95 16, 26 SMART ANTENNA ARRAY PATTERNS SYNTHESIS: NULL STEERING AND MULTI-USER BEAMFORMING BY PHASE CONTROL M. Mouhamadou and P. Vaudon IRCOM- UMR CNRS 6615, Electromagnetism and Antenna CREAPE Team - University of Limoges 123, Avenue Albert Thomas, 876 Limoges, France M. Rammal Lebanese University Radiocom Team IUT-Saida, Liban Abstract In this article, an efficient method for the pattern synthesis of the linear antenna arrays with the prescribed null and multi-lobe Beamforming is presented. Multi-lobe pattern and adaptive nulling of the pattern is achieved by controlling only the phase of each array element. The proposed method is based on the Sequential Quadratic Programming (SQP) algorithm and the linear antenna array synthesis was modelled as a multi-objective optimization problem. Multi-objective optimization is concerned with the maximization (or minimization) of a vector of objectives functions in the directions of desired signal that can be subject of a number of constraints (in our case, the constraints can be imposed as the null in the direction of interfering signal). To verify the validity of the technique, several illustrative examples of uniform excited array patterns with the main beam is placed in the direction of the useful signal and null is placed in the direction of potential interferers, and multi-beam patterns are demonstrated. 1. INTRODUCTION The reuse of spectrum in current cellular radio systems is limited by the level of co-channel interference that can be tolerated. A smart antenna has the potential to reduce multipath interferences, to increase signal
2 96 Mouhamadou, Vaudon, and Rammal to noise ratio and enhance system capacity [1, 2]. The smart antenna systems can be divided into two categories . These are: switched beam system, and adaptive arrays. In this paper, we will concentrate on the dynamically phased arrays or adaptive arrays pattern. The dynamically phased arrays make use of the Angle of Arrival (AOA) information from the desired user to steer the main beam towards the desired user . The signals received by each antenna element are weighted and combined to create a beam in the direction of the mobile. Only the phases of the weights are varied and the amplitudes are held constant. An adaptive array can adjust its antenna pattern to enhance the desired signal, null or reduce interference, and collect correlated multipath power. Adaptive array antennas can adjust their pattern to track mobile user if we including a direction of arrival (DOA) algorithm. However, several challenges remain in the development of these adaptive systems. The techniques of placing nulls in the antenna patterns to suppress interference and the maximizing their gain in the direction of desired signal has received considerable attention in the past and still of great interest [4 14]. These techniques are very important in communication system, sonar, and radar applications for maximizing signal-to-interference ratio (or signal to interference and noise ratio) . The technique of null steering including controlling the complex weights (the amplitude and phase) the excitation amplitude only and phase-only, and the element position only have been extensively considered in the literature [6, 7, 9, 14]. The phase-only is of particular interest in pattern null steering . In article  the author presents a method of control by phase for forming nulls in prescribed directions with a main lobe in broadside. The technique proposed in this paper is based on algorithm SQP  to synthesis steered beams with zero in desired direction and multi-beams patterns in the directions of the different users by phase control. This method is the generalization is the Newton method for the constrained case. They are considered the most efficient general purpose nonlinear programming algorithms today. The basic principle of sequential approximations is to replace the given nonlinear problem by a sequence of quadratic subproblems that are easier to solve. 2. PROBLEM FORMULATION Interference suppression in adaptive antenna arrays is obtained by steering beam pattern nulls in the direction of interference signal while maintaining the main lobe in the direction of user activity by adjusting the parameters positions and the current of excitation (amplitude
3 Progress In Electromagnetics Research, PIER 6, and/or phase) of the sources constituting the array. This operation of synthesis for antenna arrays in essential in the conception of an optimized antenna Multi-objective Optimization technique We consider a linear array of N equispaced isotropic antenna elements positioned along the x-axis. These antennas are supplied with same current amplitude and with a gradient of phase ϕ n. The array factor can be obtained by considering the elements to be point source which is given by: F (θ) = N 1 n= e j(kxn sin θ+ϕn) (1) Where ϕ n [ϕ,ϕ 1,...,ϕ N 1 ] represents the phase excitation of the nth element (the antenna in the beginning is taken as reference of phase: ϕ = ), x n represents the position of the nth element, k =2π/λ is the wave number, θ is the angle of incidence of desired signal or interfering signal, and λ is the signal wavelength. A general multi-objective or multicriteria problem that we study consists of a number of objectives (numbers of desired signals) and is associated with a number of inequality constraints (numbers of null steering) and bounds. Mathematically, the problem can be written as follows: Where minimize f θi (ϕ) subject to f θj (ϕ) δ j j = m e +1,...,m (2) 2π ϕ n 2π n =1,...,N 1 N 1 f θ (ϕ) = 1+ 2 e j(kxn sin θ+ϕn) ; n=1 f θi =[f θ1 f θ2 f θme ] T is the vector of objective functions, m e is the numbers of the desired signal, θ i, θ j and δ j are the ith directions of the desired signals, the jth directions of interfering signals, and the levels in the regions of the suppressed sectors respectively, and m is the number of the sampled angular direction. Note that any maximization objective can be converted into a minimization objective by simply changing its sign. The problem (2) is solved by combining the multiple objectives into one scalar objective whose solution is optimal point for the original
4 98 Mouhamadou, Vaudon, and Rammal multi-objective problem (MOP). A technique for solve the MOP is to minimize one objective while constraining the remaining objectives to be less than given target values GoalProgramming Using SequentialQuadratic Programming (SQP) Algorithm We are interested in computing the excitation phases and radiation pattern for linear antenna arrays. For this purpose, we propose, to use the goal programming combining with the SQP technique [15, 16]. In this formulation of the problem, the designer sets goals to be attained for each objective and a measure of the deviations of the objective functions from their respective goals is minimized, and the residual problem is solved by SQP algorithm. The SQP method solves a quadratic programming subproblem in each iteration which is obtained by linearizing the constraints and approximating the Lagrangian function. The Lagrangian of the problem is defined as m L(ϕ, λ) = f θ1 (ϕ)+ λ i (f θi (ϕ) δ i ) (3) i=2 Where ϕ R N 1, λ = (λ 1,...,λ m ) T R m is the vector of the Lagrange multiplier. In each iteration k of the algorithm, a quadratic subproblem minimize f θ1 (ϕ k ) T d dt M k d subject to f θi (ϕ k ) T d + f θi (ϕ k )=δ i i =2,...,m e (4) f θj (ϕ k ) T d + f θj (ϕ k ) δ j j = m e +1,...,m d R N 1 is formed, where M k is usually a positive semi-definite approximation to the Hessian matrix of the Lagrangian function with to respect to ϕ. This quadratic subproblem can be solved using any Quadratic Programming (QP) algorithm. If d k is the solution to (4) in iteration k, then the solution is used to form a new iterate ϕ k+1 = ϕ k + α k d k Where α k ], 1] is the step length parameter. We can now define the SQP algorithm: 1. set k := 1
5 Progress In Electromagnetics Research, PIER 6, solve the QP subproblem described on equation (4) to determine d k and let λ k+1 be the vector of the Lagrange multiplier of the linear constraints obtained from the QP. 3. Compute the length α k of the step and set ϕ k+1 = ϕ k + α k d k 4. Compute M k+1 from M k using a quasi-newton formula 5. Increment k. Stop if a solution is found. Otherwise, go to step NUMERICAL RESULTS To illustrate the performance of the method described in the previous section for steering single and multiple beams in desired direction, and imposed null in the direction of interfering signal by controlling the phase excitation of each array element, nine examples of uniform excited linear array with N = 1 and N = 8 one-half wavelength spaced isotropic elements were performed. The results of steering beam in the direction of the desired signal and creating single suppressed wide band interferences are presented in Figures 1, 2, 3, 4. Gain (db) Figure 1. Pattern synthesis with a single null imposed at 1 and steering lobe at 4.
6 1 Mouhamadou, Vaudon, and Rammal Gain (db) Figure 2. Pattern synthesis with a single null imposed at 15 and steering lobe at 4. Gain en (db) Figure 3. Pattern synthesis with a single null imposed at 5 and steering lobe at 2.
7 Progress In Electromagnetics Research, PIER 6, Gain en (db) Figure 4. Pattern synthesis with a single null imposed at 5 and steering lobe at 2. The Figures 1 and 2 show the ability of creating null in the direction of interference (at 1 and 15, respectively), while maintaining the main lobe in the direction of useful signal (at 4 ). In case, the interfering is fixed, the Figures 3 and 4 show that one can follow the mobile user, while maintaining the zero fixed in the direction of interference (at 5 ). The Figures 1, 3, and 4 shows that one can track at the same time the user and the interfering signals (desired signals at 4, 2, and 2, respectively, and undesired signals at 1, and 5, respectively). In this approach, the adaptive array can track the signals, and allocate beams in the direction of the useful signal while simultaneously nulling unwanted sources of interference. The phases of antenna elements are computed as given in Table 1. Also, this proposed method can create the multiple mainbeams in the directions of the different users (Figures 5, 6, 7, 8 and 9). In Figures 5 and 6, we have shown the result of a simulation with 1 isotropic elements, cancelling an interferer with DOA 6, 1, respectively and receiving signal from the user of interest with DOA 2 and 4. One of the benefits which accrue from the use of smart beams is that users residing in different beams but in the same cell are able
8 12 Mouhamadou, Vaudon, and Rammal Table 1. Computed element phases ϕ n for Figures 1, 2, 3, 4 and 5. Elem. ϕ (Degrees) No. Fig.1 Fig.2 Fig.3 Fig.4 Fig.5 n to reuse intra-cell frequency . This spatially separate of the signals, allow different users to share the same spectral resources, provided that they are spatially-separate at the base station. This Space Multiple Access (SDMA) allows multiple users to separate in the same cell, on the same frequency/time slot provided, using the adaptive antenna to separate the signals. Table 2 gives the computed element phases for the Figures 6, 7, 8 and 9 4. CONCLUSION A synthesis method for the adaptive Beamforming using the phaseonly control has been presented. The problem can be modeled as a multicriteria optimization, where the optimization objectives are the maximization of the signal at the directions of wanted sources subject to the constraints of minimization of the signal at the direction of unwanted sources. The excitation phases are computed using the Sequential Quadratic Programming (SQP) algorithm that transforms the nonlinear minimization problem to a sequence of quadratic subproblems, based on a quadratic approximation of the Lagrangian function. The simulation results show that the phase-only control using the SQP algorithm is efficient for tracking multiple users while simultaneously nulling interference.
9 Progress In Electromagnetics Research, PIER 6, Gain en (db) Figure 5. The radiation pattern with a wide sectors interference nulling around 6 and two steering lobes at 2 and 4. Gain (db) Figure 6. The radiation pattern with a wide sectors interference nulling around 1 and two steering lobes at 2 and 4.
10 14Mouhamadou, Vaudon, and Rammal Gain en (db) Figure 7. The radiation pattern with interference nulling at 3 and tree steering lobes at 6, 1 and 5. Gain en (db) Figure 8. The radiation pattern with interference nulling at 14 and tree steering lobes at 32, 2 and N =8,d= λ/2.
11 Progress In Electromagnetics Research, PIER 6, Gain en (db) Figure 9. The radiation pattern with four steering lobes at 6, 1, 28 and 48, uniform excited linear array, 24. REFERENCES 1. Joseph, C. L. and J. R. Theodore, Smart Antennas for Wireless Communications: IS 95 and Third Generation CDMA Applications, Prentice Hall, NJ, USA, Wells, M. C., Increasing the capacity of GSM cellular radio using adaptive antennas, IEE Proc. Commun., Vol. 143, No. 5, 34 31, October Lehne, P. H. and M. Pettersen, An overview of smart antenna technology for mobile communications systems, IEE Communications Surveys, Vol. 2, No. 2, 2 13, Baird, D. and G. Rassweiler, Adaptive side lobe nulling using digitally controlled phase shifters, IEEE Trans. on Antennas and Propagation, Vol. 24, No. 5, , Sept Steyskal, H., Synthesis of antenna pattern with prescribed nulls, IEEE Trans. on Antennas and Propagation, Vol. 31, , Steyskal, H., Simple method for pattern nulling by phase perturbation, IEEE Trans. on Antennas and Propagation, Vol. 31, , 1983.
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